Question: Solve for $x$ : $x^2 + 10x + 24 = 0$
Answer: The coefficient on the $x$ term is $10$ and the constant term is $24$ , so we need to find two numbers that add up to $10$ and multiply to $24$ The two numbers $6$ and $4$ satisfy both conditions: $ {6} + {4} = {10} $ $ {6} \times {4} = {24} $ $(x + {6}) (x + {4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 6) (x + 4) = 0$ $x + 6 = 0$ or $x + 4 = 0$ Thus, $x = -6$ and $x = -4$ are the solutions.